A Formal Model of Aspect Shifting: The Case of Dot Diagrams

Abstract

Many diagrams can be read in different ways, allowing readers to extract different kinds of information about the represented situation from the same representation. Such diagrams are often used to solve problems that require the combination of information from different views. This has been widely remarked upon in the literature and is sometimes referred to as aspect shifting. However, we know of no formal account of the phenomenon, or what an “aspect” of a diagram might be.

In this paper, we give such an account. In an application of our previous work, we describe a theory of representation systems in which the same representation token can be interpreted within multiple distinct representation systems. Each gives a different view of the underlying domain, accounting for multiple readability. We also describe how these different representation systems can be combined into a single overarching system which allows inference across the different aspects given by the component systems. This accounts for why just apprehending a diagram can be a substantial inferential step.